reasoning and problem solving place value year 4

Reasoning/Problem Solving Maths Worksheets for Year 4 (age 8-9)

This category is all about children choosing the most appropriate method to achieve a quick and accurate answer and to be able to explain their methods and reasoning.

Problem solving: finding the missing digits in 4-digit numbers. Tricky!

Problem solving: finding the values of missing counters. Logical thinking and careful work needed here!

Reasoning about numbers on a number line and rounding numbers.

More reasoning about number and place value.

Not only do the questions have to be answered, but explanations given. These pages really show how well children understand what they are doing.

More written explanations on which operation to use and whether the question should be done mentally or on paper.

Lots of questions, most of which can be done mentally. The important thing is to explain how they were tackled.

Decide which operation is needed (add, subtract, multiply, divide) and whether a calculator, or pencil and paper are needed, or whether it can be done, 'in your head'.

Solving problems

A selection of problem solving activities and word problems.

Here are some problems written in words. Fairly straightforward as they require just one mathematical step to work out the answer

Some word problems that need at least two steps to find the answer. This makes them much harder, so careful thinking is needed.

5 pages of word problems, all involving money. Some are suitable for calculator work as they are specially written to make the process the most important factor: it is no use having a calculator if you don't know what calculation to carry out!

A range of number and money problems, typical of those found in KS2 test papers.

More number and money problems, typical of those found in KS2 test papers.

Tricky word problems involving time and money.

More word problems; this time on measurement of length, mass and capacity. These really test children's understanding of when to use addition, subtraction, multiplication or division to solve a problem.

Time problems are especially tricky, especially when finding lengths of time that cross the hour boundary. A good knowledge of the number of days in each month is also needed.

Not many problems on a page, but there is an awful lot within each question. Each is a mini investigation, which can be explored in depth.

Number patterns, remainders, number machines and much more in this mixed selection of problems.

Working out the missing value.

More working out missing values.

Using the instructions on the packet what is the maximum number of bulbs that can be grown in the garden?

Using the instructions on the packet what is the maximum number of seeds that can be sown in the garden?

Using the instructions on the packet what is the maximum number of vegetables that can be grown in the garden?

An addition challenge suitable for year 4 on.

The fish are all called numbers. Can you work out their names by solving the clues?

Investigations

More open ended activities where children choose the approach to the task.

Making rules for sequences is an early step towards understanding algebra, and an important part of Year 5 maths. More 'How would you...?' type questions as well.

How many different three course meals can Sam choose?

Investigate patterns made by placing consecutive numbers in a number square.

A great little investigation which has plenty of extension possibilities.

Fun addition investigation using the date: 22.02.2022.

Some thoughts on how important this area of maths is.

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Resources tagged with: NC Yr 4

There are 51 NRICH Mathematical resources connected to NC Yr 4 , you may find related items under NC .

Satisfying Four Statements

Can you find any two-digit numbers that satisfy all of these statements?

Representing Numbers

Find as many different ways of representing this number of dots as you can.

Ordering Journeys

How would you put these journey lengths in order?

What Distance?

Can you use addition and subtraction to answer these questions about real-life distances?

Count Me In

How do you know whether you will reach these numbers when you count in steps of six from zero?

Dicey Operations in Line

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Seeing Squares

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Reasoned Rounding

Four strategy dice games to consolidate pupils' understanding of rounding.

Round the Dice Decimals 1

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Let Us Divide!

Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?

Discuss and Choose

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

Bryony's Triangle

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

Sorting Logic Blocks

This activity focuses on similarities and differences between shapes.

Light the Lights Again

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

A task which depends on members of the group noticing the needs of others and responding.

What Shape?

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

Counters in the Middle

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Table Patterns Go Wild!

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Times Tables Shifts

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Reflector ! Rotcelfer

Can you place the blocks so that you see the reflection in the picture?

Nice or Nasty

There are nasty versions of this dice game but we'll start with the nice ones...

The Remainders Game

Play this game and see if you can figure out the computer's chosen number.

Four-digit Targets

You have two sets of the digits 0-9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

Venn Diagrams

How will you complete these interactive Venn diagrams?

Eight Hidden Squares

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Shape Times Shape

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Multiplication Square Jigsaw

Can you complete this jigsaw of the multiplication square?

Twice as Big?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Multiples Grid

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Coordinate Challenge

Use the clues about the symmetrical properties of these letters to place them on the grid.

Torn Shapes

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

Take Your Dog for a Walk

Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?

Fractional Wall

Using the picture of the fraction wall, can you find equivalent fractions?

Stringy Quads

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Nine-pin Triangles

How many different triangles can you make on a circular pegboard that has nine pegs?

Carrying Cards

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Andy's Marbles

Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.

How Big Are Classes 5, 6 and 7?

Use the two sets of data to find out how many children there are in Classes 5, 6 and 7.

Fractional Triangles

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

The Deca Tree

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Symmetry Challenge

How many symmetric designs can you make on this grid? Can you find them all?

Let Us Reflect

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

A Cartesian Puzzle

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

Fractions in a Box

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Shapes on the Playground

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

Zios and Zepts

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

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White Rose Maths - Year 4 - Place Value - Compare and order numbers (Problem Solving and Reasoning)

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

13 August 2019

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A set of reasoning and problem solving worksheets to use alongside the White Rose Maths scheme. The questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included.

This set of worksheets are for Year 4, Autumn Block 1 (Place Value), focusing on the ninth and tenth small step of compare and order numbers. Details of how it has been differentiated can be found below: • 1 Star sheet (Working Towards Expected Level): Be able to compare and order 3 digit numbers. • 2 Star sheet (Expected Level): Be able to compare and order a 4 digit number. • 3 Star sheet (Working at greater depth): Be able to compare and order a 5 digit number.

Each worksheet contains a total of 8 questions. These questions could be used as a whole, or cut up into strips of 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children.

If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated.

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A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

White Rose Maths - Year 4 - Place Value (Problem Solving and Reasoning Practice Bundle)

A set of reasoning and problem solving worksheets to use alongside the White Rose Maths scheme. The questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included. This set of worksheets are for Year 4, Autumn Block 1 (Place Value), focusing on all the small steps. Details of how they have been differentiated can be found on their individual pages. Each worksheet contains a total of either 6 or 8 questions. These questions could be used as a whole, or cut up into strips of 3 or 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children. If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated.

White Rose Maths - Block 1 - Place Value - Steps 1 to 11 (Varied Fluency and Problem Solving Bundle)

A set of varied fluency and a set of problem solving and reasoning worksheets to use alongside the White Rose Maths scheme. Both sets of questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included. These sets of worksheets are for Year 4, Autumn Block 1 (Place value), with a set of worksheets focusing on each small step for varied fluency and problem solving and reasoning. Details of how they have been differentiated can be found on each individual set of worksheets info page. **Please note: Due to restrictions from TES on how many items can be in a bundle, I am unable to add all steps to this bundle. Steps 12 and 13 are available as a separate bundle** The varied fluency worksheets contain a total of either 6 or 8 questions, some broken down into parts (a, b, c etc.) with 3 or 4 examples of each question type. This provides children with the varied fluency that White Rose aim for. These questions can be used as a quick starter and cut up so that only the first 3 or 4 questions are used, or given as more of a main activity with all 6 or 8 questions. They could also be used for partner work, depending on the ability of the children. The problem solving and reasoning worksheets contain a total of either 6 or 8 questions. These questions could be used as a whole, or cut up into strips of 3 or 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children. If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated.

White Rose Maths - Year 4- Place Value - Compare and order numbers (Varied Fluency and Problem Solving)

A set of varied fluency and a set of problem solving and reasoning worksheets to use alongside the White Rose Maths scheme. Both sets of questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included. This set of worksheets are for Year 4, Autumn Block 1 (Place Value), focusing on the ninth and tenth small steps of compare and order numbers. Details of how they have been differentiated can be found below: • 1 Star sheet (Working Towards Expected Level): Be able to compare and order 3 digit numbers. • 2 Star sheet (Expected Level): Be able to compare and order a 4 digit number. • 3 Star sheet (Working at greater depth): Be able to compare and order a 5 digit number. The varied fluency worksheets contain a total of 6 questions, some broken down into parts (a and b) with 3 examples of each question type. This provides children with the varied fluency that White Rose aim for. These questions can be used as a quick starter and cut up so that only the first 3 questions are used or given as more of a main activity with all 6 questions. They could also be used for partner work, depending on the ability of the children. The problem solving and reasoning worksheets contain a total of 8 questions. These questions could be used as a whole or cut up into strips of 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children. If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated.

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